lgcp

Description

An R package for spatiotemporal prediction and forecasting for log-Gaussian Cox processes.

Usage

lgcp

Format

An object of class logical of length 1.

Details

This package was not yet installed at build time.
Index: This package was not yet installed at build time.

For examples and further details of the package, type vignette("lgcp"), or refer to the paper associated with this package.

The content of lgcp can be broken up as follows:

Datasets wpopdata.rda, wtowncoords.rda, wtowns.rda. Giving regional and town poopulations as well as town coordinates,are provided by Wikipedia and The Office for National Statistics under respectively the Creative Commons Attribution-ShareAlike 3.0 Unported License and the Open Government Licence.

Data manipulation

Model fitting and parameter estimation

Unconditional and conditional simulation

Summary statistics, diagnostics and visualisation

Dependencies

The lgcp package depends upon some other important contributions to CRAN in order to operate; their uses here are indicated:

spatstat, sp, RandomFields, iterators, ncdf, methods, tcltk, rgl, rpanel, fields, rgdal, maptools, rgeos, raster

Citation

To see how to cite lgcp, type citation("lgcp") at the console.

Author(s)

Benjamin Taylor, Health and Medicine, Lancaster University, Tilman Davies, Institute of Fundamental Sciences - Statistics, Massey University, New Zealand., Barry Rowlingson, Health and Medicine, Lancaster University Peter Diggle, Health and Medicine, Lancaster University

References

1. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

2. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

3. Wood ATA, Chan G (1994). Simulation of Stationary Gaussian Processes in [0,1]d. Journal of Computational and Graphical Statistics, 3(4), 409-432.

4. Moller J, Syversveen AR, Waagepetersen RP (1998). Log Gaussian Cox Processes. Scandinavian Journal of Statistics, 25(3), 451-482.

.onAttach function

Description

A function to print a welcome message on loading package

Usage

.onAttach(libname, pkgname)

Arguments

Value

...

BetaParameters function

Description

An internal function to declare a vector a parameter vector for the main effects.

Usage

BetaParameters(beta)

Arguments

Value

...

CovFunction function

Description

A Generic method used to specify the choice of covariance function for use in the MCMC algorithm. For further details and examples, see the vignette "Bayesian_lgcp".

Usage

CovFunction(obj, ...)

Arguments

Value

method CovFunction

See Also

CovFunction.function, exponentialCovFct, RandomFieldsCovFct, SpikedExponentialCovFct

CovFunction.function function

Description

A function used to define the covariance function for the latent field prior to running the MCMC algorithm

Usage

## S3 method for class ''function''
CovFunction(obj, ...)

Arguments

Value

the covariance function ready to run the MCMC routine.

See Also

exponentialCovFct, RandomFieldsCovFct, SpikedExponentialCovFct, CovarianceFct

Examples

## Not run: cf1 <- CovFunction(exponentialCovFct)
## Not run: cf2 <- CovFunction(RandomFieldsCovFct(model="matern",additionalparameters=1))

CovParameters function

Description

A function to provide a structure for the parameters of the latent field. Not intended for general use.

Usage

CovParameters(list)

Arguments

Value

an object used in the MCMC routine.

CovarianceFct function

Description

A function to

Usage

CovarianceFct(u, sigma, phi, model, additionalparameters)

Arguments

Value

the covariance function evaluated at the specified distances

Cvb function

Description

This function is used in thetaEst to estimate the temporal correlation parameter, theta.

Usage

Cvb(xyt, spatial.intensity, N = 100, spatial.covmodel, covpars)

Arguments

Value

a function, see below. Computes Monte carlo estimate of function C(v;beta) in Brix and Diggle 2001 pp 829 (... note later corrigendum to paper (2003) corrects the expression given in this paper)

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

See Also

thetaEst

EvaluatePrior function

Description

An internal function used in the MCMC routine to evaluate the prior for a given set of parameters

Usage

EvaluatePrior(etaParameters, betaParameters, prior)

Arguments

Value

the prior evaluated at the given values.

Extract.mstppp function

Description

extracting subsets of an mstppp object.

Usage

"x[subset]"

Arguments

Value

extracts subset of an mstppp object

Extract.stppp function

Description

extracting subsets of an stppp object.

Usage

"x[subset]"

Arguments

Value

extracts subset of an stppp object

Examples

## Not run: xyt <- lgcpSim()
## Not run: xyt
## Not run: xyt[xyt$t>0.5]

GAfinalise function

Description

Generic function defining the the finalisation step for the gridAverage class of functions. The function is called invisibly within MALAlgcp and facilitates the computation of Monte Carlo Averages online.

Usage

GAfinalise(F, ...)

Arguments

Value

method GAfinalise

See Also

setoutput, GAinitialise, GAupdate, GAreturnvalue

GAfinalise.MonteCarloAverage function

Description

Finalise a Monte Carlo averaging scheme. Divide the sum by the number of iterations.

Usage

## S3 method for class 'MonteCarloAverage'
GAfinalise(F, ...)

Arguments

Value

computes Monte Carlo averages

See Also

MonteCarloAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GAfinalise.nullAverage function

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullAverage'
GAfinalise(F, ...)

Arguments

Value

nothing

See Also

nullAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GAinitialise function

Description

Generic function defining the the initialisation step for the gridAverage class of functions. The function is called invisibly within MALAlgcp and facilitates the computation of Monte Carlo Averages online.

Usage

GAinitialise(F, ...)

Arguments

Value

method GAinitialise

See Also

setoutput, GAupdate, GAfinalise, GAreturnvalue

GAinitialise.MonteCarloAverage function

Description

Initialise a Monte Carlo averaging scheme.

Usage

## S3 method for class 'MonteCarloAverage'
GAinitialise(F, ...)

Arguments

Value

nothing

See Also

MonteCarloAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GAinitialise.nullAverage function

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullAverage'
GAinitialise(F, ...)

Arguments

Value

nothing

See Also

nullAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GAreturnvalue function

Description

Generic function defining the the returned value for the gridAverage class of functions. The function is called invisibly within MALAlgcp and facilitates the computation of Monte Carlo Averages online.

Usage

GAreturnvalue(F, ...)

Arguments

Value

method GAreturnvalue

See Also

setoutput, GAinitialise, GAupdate, GAfinalise

GAreturnvalue.MonteCarloAverage function

Description

Returns the required Monte Carlo average.

Usage

## S3 method for class 'MonteCarloAverage'
GAreturnvalue(F, ...)

Arguments

Value

results from MonteCarloAverage

See Also

MonteCarloAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GAreturnvalue.nullAverage function##'

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullAverage'
GAreturnvalue(F, ...)

Arguments

Value

nothing

See Also

nullAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GAupdate function

Description

Generic function defining the the update step for the gridAverage class of functions. The function is called invisibly within MALAlgcp and facilitates the computation of Monte Carlo Averages online.

Usage

GAupdate(F, ...)

Arguments

Value

method GAupdate

See Also

setoutput, GAinitialise, GAfinalise, GAreturnvalue

GAupdate.MonteCarloAverage function

Description

Update a Monte Carlo averaging scheme. This function performs the Monte Carlo sum online.

Usage

## S3 method for class 'MonteCarloAverage'
GAupdate(F, ...)

Arguments

Value

updates Monte Carlo sums

See Also

MonteCarloAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GAupdate.nullAverage function

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullAverage'
GAupdate(F, ...)

Arguments

Value

nothing

See Also

nullAverage, setoutput, GAinitialise, GAupdate, GAfinalise, GAreturnvalue

GFfinalise function

Description

Generic function defining the the finalisation step for the gridFunction class of objects. The function is called invisibly within MALAlgcp and facilitates the dumping of data to disk

Usage

GFfinalise(F, ...)

Arguments

Value

method GFfinalise

See Also

setoutput, GFinitialise, GFupdate, GFreturnvalue

GFfinalise.dump2dir function

Description

This function finalises the dumping of data to a netCDF file.

Usage

## S3 method for class 'dump2dir'
GFfinalise(F, ...)

Arguments

Value

nothing

See Also

dump2dir, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GFfinalise.nullFunction function

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullFunction'
GFfinalise(F, ...)

Arguments

Value

nothing

See Also

nullFunction, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GFinitialise function

Description

Generic function defining the the initialisation step for the gridFunction class of objects. The function is called invisibly within MALAlgcp and facilitates the dumping of data to disk

Usage

GFinitialise(F, ...)

Arguments

Value

method GFinitialise

See Also

setoutput, GFupdate, GFfinalise, GFreturnvalue

GFinitialise.dump2dir function

Description

Creates a directory (if necessary) and allocates space for a netCDF dump.

Usage

## S3 method for class 'dump2dir'
GFinitialise(F, ...)

Arguments

Value

creates initialisation file and folder

See Also

dump2dir, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GFinitialise.nullFunction function

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullFunction'
GFinitialise(F, ...)

Arguments

Value

nothing

See Also

nullFunction, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GFreturnvalue function

Description

Generic function defining the the returned value for the gridFunction class of objects. The function is called invisibly within MALAlgcp and facilitates the dumping of data to disk

Usage

GFreturnvalue(F, ...)

Arguments

Value

method GFreturnvalue

See Also

setoutput, GFinitialise, GFupdate, GFfinalise

GFreturnvalue.dump2dir function

Description

This function returns the name of the directory the netCDF file was written to.

Usage

## S3 method for class 'dump2dir'
GFreturnvalue(F, ...)

Arguments

Value

display where files have been written to

See Also

dump2dir, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GFreturnvalue.nullFunction function

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullFunction'
GFreturnvalue(F, ...)

Arguments

Value

nothing

See Also

nullFunction, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GFupdate function

Description

Generic function defining the the update step for the gridFunction class of objects. The function is called invisibly within MALAlgcp and facilitates the dumping of data to disk

Usage

GFupdate(F, ...)

Arguments

Value

method GFupdate

See Also

setoutput, GFinitialise, GFfinalise, GFreturnvalue

GFupdate.dump2dir function

Description

This function gets the required information from MALAlgcp and writes the data to the netCDF file.

Usage

## S3 method for class 'dump2dir'
GFupdate(F, ...)

Arguments

Value

saves latent field

See Also

dump2dir, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GFupdate.nullFunction function

Description

This is a null function and performs no action.

Usage

## S3 method for class 'nullFunction'
GFupdate(F, ...)

Arguments

Value

nothing

See Also

nullFunction, setoutput, GFinitialise, GFupdate, GFfinalise, GFreturnvalue

GPdrv function

Description

A function to compute the first derivatives of the log target with respect to the paramters of the latent field. Not intended for general purpose use.

Usage

GPdrv(
  GP,
  prior,
  Z,
  Zt,
  eta,
  beta,
  nis,
  cellarea,
  spatial,
  gradtrunc,
  fftgrid,
  covfunction,
  d,
  eps = 1e-06
)

Arguments

Value

first derivatives of the log target at the specified paramters Y, eta and beta

GPdrv2 function

Description

A function to compute the second derivative of the log target with respect to the paramters of the latent field. Not intended for general purpose use.

Usage

GPdrv2(
  GP,
  prior,
  Z,
  Zt,
  eta,
  beta,
  nis,
  cellarea,
  spatial,
  gradtrunc,
  fftgrid,
  covfunction,
  d,
  eps = 1e-06
)

Arguments

Value

first and second derivatives of the log target at the specified paramters Y, eta and beta

GPdrv2_Multitype function

Description

A function to compute the second derivatives of the log target for the multivariate model with respect to the paramters of the latent field. Not intended for general use.

Usage

GPdrv2_Multitype(
  GPlist,
  priorlist,
  Zlist,
  Ztlist,
  etalist,
  betalist,
  nis,
  cellarea,
  spatial,
  gradtrunc,
  fftgrid,
  covfunction,
  d,
  eps = 1e-06,
  k
)

Arguments

Value

first and second derivatives of the log target for tyupe k at the specified paramters Y, eta and beta

GPlist2array function

Description

An internal function for turning a list of GPrealisation objects into an an array by a particular common element of the GPrealisation object

Usage

GPlist2array(GPlist, element)

Arguments

Value

an array

GPrealisation function

Description

A function to store a realisation of a spatial gaussian process for use in MCMC algorithms that include Bayesian parameter estimation. Stores not only the realisation, but also computational quantities.

Usage

GPrealisation(gamma, fftgrid, covFunction, covParameters, d)

Arguments

Value

a realisation of a spatial Gaussian process on a regular grid

GammafromY function

Description

A function to change Ys (spatially correlated noise) into Gammas (white noise). Used in the MALA algorithm.

Usage

GammafromY(Y, rootQeigs, mu)

Arguments

Value

Gamma

GaussianPrior function

Description

A function to create a Gaussian prior.

Usage

GaussianPrior(mean, variance)

Arguments

Value

an object of class LogGaussianPrior that can be passed to the function PriorSpec.

See Also

LogGaussianPrior, linkPriorSpec.list

Examples

## Not run: GaussianPrior(mean=rep(0,9),variance=diag(10^6,9))

KinhomAverage function

Description

A function to estimate the inhomogeneous K function for a spatiotemporal point process. The method of computation is similar to ginhomAverage, see eq (8) Diggle P, Rowlingson B, Su T (2005) to see how this is computed.

Usage

KinhomAverage(
  xyt,
  spatial.intensity,
  temporal.intensity,
  time.window = xyt$tlim,
  rvals = NULL,
  correction = "iso",
  suppresswarnings = FALSE
)

Arguments

Value

time average of inhomogenous K function.

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Baddeley AJ, Moller J, Waagepetersen R (2000). Non-and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54, 329-350.

3. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

4. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

See Also

ginhomAverage, spatialparsEst, thetaEst, lambdaEst, muEst

LogGaussianPrior function

Description

A function to create a Gaussian prior on the log scale

Usage

LogGaussianPrior(mean, variance)

Arguments

Value

an object of class LogGaussianPrior that can be passed to the function PriorSpec.

See Also

GaussianPrior, linkPriorSpec.list

Examples

## Not run: LogGaussianPrior(mean=log(c(1,500)),variance=diag(0.15,2))

MALAlgcp function

Description

ADVANCED USE ONLY A function to perform MALA for the spatial only case

Usage

MALAlgcp(
  mcmcloop,
  inits,
  adaptivescheme,
  M,
  N,
  Mext,
  Next,
  sigma,
  phi,
  theta,
  mu,
  nis,
  cellarea,
  spatialvals,
  temporal.fitted,
  tdiff,
  scaleconst,
  rootQeigs,
  invrootQeigs,
  cellInside,
  MCMCdiag,
  gradtrunc,
  gridfun,
  gridav,
  mcens,
  ncens,
  aggtimes
)

Arguments

Value

object passed back to lgcpPredictSpatial

MALAlgcpAggregateSpatial.PlusPars function

Description

A function to run the MCMC algorithm for aggregated spatial point process data. Not for general purpose use.

Usage

MALAlgcpAggregateSpatial.PlusPars(
  mcmcloop,
  inits,
  adaptivescheme,
  M,
  N,
  Mext,
  Next,
  mcens,
  ncens,
  formula,
  Zmat,
  model.priors,
  model.inits,
  fftgrid,
  spatial.covmodel,
  nis,
  cellarea,
  spatialvals,
  cellInside,
  MCMCdiag,
  gradtrunc,
  gridfun,
  gridav,
  d,
  spdf,
  ol,
  Nfreq
)

Arguments

Value

output from the MCMC run

MALAlgcpMultitypeSpatial.PlusPars function

Description

A function to run the MCMC algorithm for multivariate spatial point process data. Not for general purpose use.

Usage

MALAlgcpMultitypeSpatial.PlusPars(
  mcmcloop,
  inits,
  adaptivescheme,
  M,
  N,
  Mext,
  Next,
  mcens,
  ncens,
  formulaList,
  zml,
  Zmat,
  model.priorsList,
  model.initsList,
  fftgrid,
  spatial.covmodelList,
  nis,
  cellarea,
  spatialvals,
  cellInside,
  MCMCdiag,
  gradtrunc,
  gridfun,
  gridav,
  marks,
  ntypes,
  d
)

Arguments

Value

output from the MCMC run

MALAlgcpSpatial function

Description

ADVANCED USE ONLY A function to perform MALA for the spatial only case

Usage

MALAlgcpSpatial(
  mcmcloop,
  inits,
  adaptivescheme,
  M,
  N,
  Mext,
  Next,
  sigma,
  phi,
  mu,
  nis,
  cellarea,
  spatialvals,
  scaleconst,
  rootQeigs,
  invrootQeigs,
  cellInside,
  MCMCdiag,
  gradtrunc,
  gridfun,
  gridav,
  mcens,
  ncens
)

Arguments

Value

object passed back to lgcpPredictSpatial

MALAlgcpSpatial.PlusPars function

Description

A function to run the MCMC algorithm for spatial point process data. Not for general purpose use.

Usage

MALAlgcpSpatial.PlusPars(
  mcmcloop,
  inits,
  adaptivescheme,
  M,
  N,
  Mext,
  Next,
  mcens,
  ncens,
  formula,
  Zmat,
  model.priors,
  model.inits,
  fftgrid,
  spatial.covmodel,
  nis,
  cellarea,
  spatialvals,
  cellInside,
  MCMCdiag,
  gradtrunc,
  gridfun,
  gridav,
  d
)

Arguments

Value

output from the MCMC run

MALAlgcpSpatioTemporal.PlusPars function

Description

A function to run the MCMC algorithm for spatiotemporal point process data. Not for general purpose use.

Usage

MALAlgcpSpatioTemporal.PlusPars(
  mcmcloop,
  inits,
  adaptivescheme,
  M,
  N,
  Mext,
  Next,
  mcens,
  ncens,
  formula,
  ZmatList,
  model.priors,
  model.inits,
  fftgrid,
  spatial.covmodel,
  nis,
  tdiff,
  cellarea,
  spatialvals,
  cellInside,
  MCMCdiag,
  gradtrunc,
  gridfun,
  gridav,
  d,
  aggtimes,
  spatialOnlyCovariates
)

Arguments

Value

output from the MCMC run

MonteCarloAverage function

Description

This function creates an object of class MonteCarloAverage. The purpose of the function is to compute Monte Carlo expectations online in the function lgcpPredict, it is set in the argument gridmeans of the argument output.control.

Usage

MonteCarloAverage(funlist, lastonly = TRUE)

Arguments

Details

A Monte Carlo Average is computed as:

E_{\pi(Y_{t_1:t_2}|X_{t_1:t_2})}[g(Y_{t_1:t_2})] \approx \frac1n\sum_{i=1}^n g(Y_{t_1:t_2}^{(i)})

where g is a function of interest, Y_{t_1:t_2}^{(i)} is the ith retained sample from the target and n is the total number of retained iterations. For example, to compute the mean of Y_{t_1:t_2} set,

g(Y_{t_1:t_2}) = Y_{t_1:t_2},

the output from such a Monte Carlo average would be a set of t_2-t_1 grids, each cell of which being equal to the mean over all retained iterations of the algorithm (NOTE: this is just an example computation, in practice, there is no need to compute the mean on line explicitly, as this is already done by defaul in lgcpPredict). For further examples, see below. The option last=TRUE computes,

E_{\pi(Y_{t_1:t_2}|X_{t_1:t_2})}[g(Y_{t_2})],

so in this case the expectation over the last time point only is computed. This can save computation time.

Value

object of class MonteCarloAverage

See Also

setoutput, lgcpPredict, GAinitialise, GAupdate, GAfinalise, GAreturnvalue, exceedProbs

Examples

fun1 <- function(x){return(x)}   # gives the mean
fun2 <- function(x){return(x^2)} # computes E(X^2). Can be used with the 
                                 # mean to compute variances, since 
                                 # Var(X) = E(X^2) - E(X)^2
fun3 <- exceedProbs(c(1.5,2,3))  # exceedance probabilities, 
                                 #see ?exceedProbs
mca <- MonteCarloAverage(c("fun1","fun2","fun3"))
mca2 <- MonteCarloAverage(c("fun1","fun2","fun3"),lastonly=TRUE)

PriorSpec function

Description

Generic for declaring that an object is of valid type for use as as prior in lgcp. For further details and examples, see the vignette "Bayesian_lgcp".

Usage

PriorSpec(obj, ...)

Arguments

Value

method PriorSpec

See Also

PriorSpec.list

PriorSpec.list function

Description

Method for declaring a Bayesian prior density in lgcp. Checks to confirm that the object obj has the requisite components for functioning as a prior.

Usage

## S3 method for class 'list'
PriorSpec(obj, ...)

Arguments

Value

an object suitable for use in a call to the MCMC routines

See Also

GaussianPrior, LogGaussianPrior

Examples

## Not run: PriorSpec(LogGaussianPrior(mean=log(c(1,500)),variance=diag(0.15,2)))
## Not run: PriorSpec(GaussianPrior(mean=rep(0,9),variance=diag(10^6,9)))

RandomFieldsCovFct function

Description

A function to declare and also evaluate an covariance function from the RandomFields Package. See ?CovarianceFct. Note that the present version of lgcp only offers estimation for sigma and phi, any additional paramters are treated as fixed.

Usage

RandomFieldsCovFct(model, additionalparameters = c())

Arguments

Value

a covariance function from the RandomFields package

See Also

CovFunction.function, exponentialCovFct, SpikedExponentialCovFct, CovarianceFct

Examples

## Not run: RandomFieldsCovFct(model="matern",additionalparameters=1)

SpatialPolygonsDataFrame.stapp function

Description

A function to return the SpatialPolygonsDataFrame part of an stapp object

Usage

SpatialPolygonsDataFrame.stapp(from)

Arguments

Value

an object of class SpatialPolygonsDataFrame

SpikedExponentialCovFct function

Description

A function to declare and also evaluate a spiked exponential covariance function. Note that the present version of lgcp only offers estimation for sigma and phi, the additional parameter 'spikevar' is treated as fixed.

Usage

SpikedExponentialCovFct(d, CovParameters, spikevar = 1)

Arguments

Value

the spiked exponential covariance function; note that the spikevariance is currently not estimated as part of the MCMC routine, and is thus treated as a fixed parameter.

See Also

CovFunction.function, exponentialCovFct, RandomFieldsCovFct

YfromGamma function

Description

A function to change Gammas (white noise) into Ys (spatially correlated noise). Used in the MALA algorithm.

Usage

YfromGamma(Gamma, invrootQeigs, mu)

Arguments

Value

Y

add.list function

Description

This function adds the elements of two list objects together and returns the result in another list object.

Usage

add.list(list1, list2)

Arguments

Value

a list with ith entry the sum of list1[[i]] and list2[[i]]

addTemporalCovariates function

Description

A function to 'bolt on' temporal data onto a spatial covariate design matrix. The function takes a spatial design matrix, Z(s) and converts it to a spatiotemporal design matrix Z(s,t) when the effects can be separably decomposed i.e.,
Z(s,t)beta = Z_1(s)beta_1 + Z_2(t)beta_2

An example of this function in action is given in the vignette "Bayesian_lgcp", in the section on spatiotemporal data.

Usage

addTemporalCovariates(temporal.formula, T, laglength, tdata, Zmat)

Arguments

Details

The main idea of this function is: having created a spatial Z(s) using getZmat, to create a dummy dataset tdata and temporal formula corresponding to the temporal component of the separable effects. The entries in the model matrix Z(s,t) corresponsing to the time covariates are constant over the observation window in space, but in general vary from time-point to time-point.

Note that if there is an intercept in the spatial part of the model e.g., X ~ var1 + var2, then in the temporal model, the intercept should be removed i.e., t ~ tvar1 + tvar2 - 1

Value

A list of design matrices, one for each time, Z(s,t) for t in (T-laglength):T

See Also

chooseCellwidth, getpolyol, guessinterp, getZmat, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

affine.SpatialPolygonsDataFrame function

Description

An affine transformation of an object of class SpatialPolygonsDataFrame

Usage

## S3 method for class 'SpatialPolygonsDataFrame'
affine(X, mat, ...)

Arguments

Value

the object acted on by the transformation matrix

affine.fromFunction function

Description

An affine transformation of an object of class fromFunction

Usage

## S3 method for class 'fromFunction'
affine(X, mat, ...)

Arguments

Value

the object acted on by the transformation matrix

affine.fromSPDF function

Description

An affine transformation of an object of class fromSPDF

Usage

## S3 method for class 'fromSPDF'
affine(X, mat, ...)

Arguments

Value

the object acted on by the transformation matrix

affine.fromXYZ function

Description

An affine transformation of an object of class fromXYZ. Nearest Neighbour interpolation

Usage

## S3 method for class 'fromXYZ'
affine(X, mat, ...)

Arguments

Value

the object acted on by the transformation matrix

affine.stppp function

Description

An affine transformation of an object of class stppp

Usage

## S3 method for class 'stppp'
affine(X, mat, ...)

Arguments

Value

the object acted on by the transformation matrix

aggCovInfo function

Description

Generic function for aggregation of covariate information.

Usage

aggCovInfo(obj, ...)

Arguments

Value

method aggCovInfo

aggCovInfo.ArealWeightedMean function

Description

Aggregation via weighted mean.

Usage

## S3 method for class 'ArealWeightedMean'
aggCovInfo(obj, regwts, ...)

Arguments

Value

Areal weighted mean.

aggCovInfo.ArealWeightedSum function

Description

Aggregation via weighted sum. Use to sum up population counts in regions.

Usage

## S3 method for class 'ArealWeightedSum'
aggCovInfo(obj, regwts, ...)

Arguments

Value

Areal weighted Sum.

aggCovInfo.Majority function

Description

Aggregation via majority.

Usage

## S3 method for class 'Majority'
aggCovInfo(obj, regwts, ...)

Arguments

Value

The most popular cell type.

aggregateCovariateInfo function

Description

A function called by cov.interp.fft to allocate and perform interpolation of covariate infomation onto the FFT grid

Usage

aggregateCovariateInfo(cellidx, cidx, gidx, df, fftovl, classes, polyareas)

Arguments

Value

the interpolated covariate information onto the FFT grid

aggregateformulaList function

Description

An internal function to collect terms from a formulalist. Not intended for general use.

Usage

aggregateformulaList(x, ...)

Arguments

Value

a formula of the form X ~ var1 + var2 tec.

andrieuthomsh function

Description

A Robbins-Munro stochastic approximation update is used to adapt the tuning parameter of the proposal kernel. The idea is to update the tuning parameter at each iteration of the sampler:

h^{(i+1)} = h^{(i)} + \eta^{(i+1)}(\alpha^{(i)} - \alpha_{opt}),

where h^{(i)} and \alpha^{(i)} are the tuning parameter and acceptance probability at iteration i and \alpha_{opt} is a target acceptance probability. For Gaussian targets, and in the limit as the dimension of the problem tends to infinity, an appropriate target acceptance probability for MALA algorithms is 0.574. The sequence \{\eta^{(i)}\} is chosen so that \sum_{i=0}^\infty\eta^{(i)} is infinite whilst \sum_{i=0}^\infty\left(\eta^{(i)}\right)^{1+\epsilon} is finite for \epsilon>0. These two conditions ensure that any value of h can be reached, but in a way that maintains the ergodic behaviour of the chain. One class of sequences with this property is,

\eta^{(i)} = \frac{C}{i^\alpha},

where \alpha\in(0,1] and C>0.The scheme is set via the mcmcpars function.

Usage

andrieuthomsh(inith, alpha, C, targetacceptance = 0.574)

Arguments

Value

an object of class andrieuthomsh

References

1. Andrieu C, Thoms J (2008). A tutorial on adaptive MCMC. Statistics and Computing, 18(4), 343-373.

2. Robbins H, Munro S (1951). A Stochastic Approximation Methods. The Annals of Mathematical Statistics, 22(3), 400-407.

3. Roberts G, Rosenthal J (2001). Optimal Scaling for Various Metropolis-Hastings Algorithms. Statistical Science, 16(4), 351-367.

See Also

mcmcpars, lgcpPredict

Examples

andrieuthomsh(inith=1,alpha=0.5,C=1,targetacceptance=0.574)

as.SpatialGridDataFrame function

Description

Generic method for convertign to an object of class SpatialGridDataFrame.

Usage

as.SpatialGridDataFrame(obj, ...)

Arguments

Value

method as.SpatialGridDataFrame

See Also

as.SpatialGridDataFrame.fromXYZ

as.SpatialGridDataFrame.fromXYZ function

Description

Method for converting objects of class fromXYZ into those of class SpatialGridDataFrame

Usage

## S3 method for class 'fromXYZ'
as.SpatialGridDataFrame(obj, ...)

Arguments

Value

an object of class SpatialGridDataFrame

See Also

as.SpatialGridDataFrame

as.SpatialPixelsDataFrame function

Description

Generic function for conversion to SpatialPixels objects.

Usage

as.SpatialPixelsDataFrame(obj, ...)

Arguments

Value

method as.SpatialPixels

See Also

as.SpatialPixelsDataFrame.lgcpgrid

as.SpatialPixelsDataFrame.lgcpgrid function

Description

Method to convert lgcpgrid objects to SpatialPixelsDataFrame objects.

Usage

## S3 method for class 'lgcpgrid'
as.SpatialPixelsDataFrame(obj, ...)

Arguments

Value

Either a SpatialPixelsDataFrame, or a list consisting of SpatialPixelsDataFrame objects.

as.array.lgcpgrid function

Description

Method to convert an lgcpgrid object into an array.

Usage

## S3 method for class 'lgcpgrid'
as.array(x, ...)

Arguments

Value

conversion from lgcpgrid to array

as.fromXYZ function

Description

Generic function for conversion to a fromXYZ object (eg as would have been produced by spatialAtRisk for example.)

Usage

as.fromXYZ(X, ...)

Arguments

Value

generic function returning method as.fromXYZ

See Also

as.im.fromXYZ, as.im.fromSPDF, as.im.fromFunction, as.fromXYZ

as.fromXYZ.fromFunction function

Description

Method for converting from the fromFunction class of objects to the fromXYZ class of objects. Clearly this requires the user to specify a grid onto which to compute the discretised verion.

Usage

## S3 method for class 'fromFunction'
as.fromXYZ(X, xyt, M = 100, N = 100, ...)

Arguments

Value

object of class im containing normalised intensities

See Also

as.im.fromXYZ, as.im.fromSPDF, as.im.fromFunction, as.fromXYZ

as.im.fromFunction function

Description

Convert an object of class fromFunction(created by spatialAtRisk for example) into a spatstat im object.

Usage

## S3 method for class 'fromFunction'
as.im(X, xyt, M = 100, N = 100, ...)

Arguments

Value

object of class im containing normalised intensities

See Also

as.im.fromXYZ, as.im.fromSPDF, as.im.fromFunction, as.fromXYZ

as.im.fromSPDF function

Description

Convert an object of class fromSPDF (created by spatialAtRisk for example) into a spatstat im object.

Usage

## S3 method for class 'fromSPDF'
as.im(X, ncells = 100, ...)

Arguments

Value

object of class im containing normalised intensities

See Also

as.im.fromXYZ, as.im.fromSPDF, as.im.fromFunction, as.fromXYZ

as.im.fromXYZ function

Description

Convert an object of class fromXYZ (created by spatialAtRisk for example) into a spatstat im object.

Usage

## S3 method for class 'fromXYZ'
as.im(X, ...)

Arguments

Value

object of class im containing normalised intensities

See Also

as.im.fromSPDF, as.im.fromFunction, as.fromXYZ

as.list.lgcpgrid function

Description

Method to convert an lgcpgrid object into a list of matrices.

Usage

## S3 method for class 'lgcpgrid'
as.list(x, ...)

Arguments

Value

conversion from lgcpgrid to list

See Also

lgcpgrid.list, lgcpgrid.array, print.lgcpgrid, summary.lgcpgrid, quantile.lgcpgrid, image.lgcpgrid, plot.lgcpgrid

as.owin.stapp function

Description

A function to extract the SpatialPolygons part of W and return it as an owin object.

Usage

## S3 method for class 'stapp'
as.owin(W, ..., fatal = TRUE)

Arguments

Value

an owin object

as.owinlist function

Description

Generic function for creating lists of owin objects

Usage

as.owinlist(obj, ...)

Arguments

Value

method as.owinlist

as.owinlist.SpatialPolygonsDataFrame function

Description

A function to create a list of owin objects from a SpatialPolygonsDataFrame

Usage

## S3 method for class 'SpatialPolygonsDataFrame'
as.owinlist(obj, dmin = 0, check = TRUE, subset = rep(TRUE, length(obj)), ...)

Arguments

Value

a list of owin objects corresponding to the constituent Polygons objects

as.owinlist.stapp function

Description

A function to create a list of owin objects from a stapp

Usage

## S3 method for class 'stapp'
as.owinlist(obj, dmin = 0, check = TRUE, ...)

Arguments

Value

a list of owin objects corresponding to the constituent Polygons objects

as.ppp.mstppp function

Description

Convert from mstppp to ppp. Can be useful for data handling.

Usage

## S3 method for class 'mstppp'
as.ppp(X, ..., fatal = TRUE)

Arguments

Value

a ppp object without observation times

as.ppp.stppp function

Description

Convert from stppp to ppp. Can be useful for data handling.

Usage

## S3 method for class 'stppp'
as.ppp(X, ..., fatal = TRUE)

Arguments

Value

a ppp object without observation times

as.stppp function

Description

Generic function for converting to stppp objects

Usage

as.stppp(obj, ...)

Arguments

Value

method as.stppp

as.stppp.stapp function

Description

A function to convert stapp objects to stppp objects for use in lgcpPredict. The regional counts in the stapp object are assigned a random location within each areal region proportional to a population density (if that is available) else the counts are distributed uniformly across the observation windows.

Usage

## S3 method for class 'stapp'
as.stppp(obj, popden = NULL, n = 100, dmin = 0, check = TRUE, ...)

Arguments

Value

...

assigninterp function

Description

A function to assign an interpolation type to a variable in a data frame.

Usage

assigninterp(df, vars, value)

Arguments

Details

The three types of interpolation method employed in the package lgcp are:

1. 'Majority' The interpolated value corresponds to the value of the covariate occupying the largest area of the computational cell.

2. 'ArealWeightedMean' The interpolated value corresponds to the mean of all covariate values contributing to the computational cell weighted by their respective areas.

3. 'ArealWeightedSum' The interpolated value is the sum of all contributing covariates weighed by the proportion of area with respect to the covariate polygons. For example, suppose region A has the same area as a computational grid cell and has 500 inhabitants. If that region occupies half of a computational grid cell, then this interpolation type assigns 250 inhabitants from A to the computational grid cell.

Value

assigns an interpolation type to a variable

See Also

chooseCellwidth, getpolyol, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

Examples

## Not run: spdf a SpatialPolygonsDataFrame
## Not run: spdf@data <- assigninterp(df=spdf@data,vars="pop",value="ArealWeightedSum")

at function

Description

at function

Usage

at(t, mu, theta)

Arguments

Value

...

autocorr function

Description

This function requires data to have been dumped to disk: see ?dump2dir and ?setoutput. The routine autocorr.lgcpPredict computes cellwise selected autocorrelations of Y. Since computing the quantiles is an expensive operation, the option to output the quantiles on a subregion of interest is also provided (by setting the argument inWindow, which has a sensible default).

Usage

autocorr(
  x,
  lags,
  tidx = NULL,
  inWindow = x$xyt$window,
  crop2parentwindow = TRUE,
  ...
)

Arguments

Value

an array, the [,,i]th slice being the grid of cell-wise autocorrelations.

See Also

lgcpPredict, dump2dir, setoutput, plot.lgcpAutocorr, ltar, parautocorr, traceplots, parsummary, textsummary, priorpost, postcov, exceedProbs, betavals, etavals

autocorrMultitype function

Description

A function to compute cell-wise autocorrelation in the latent field at specifiec lags

Usage

autocorrMultitype(
  x,
  lags,
  fieldno,
  inWindow = x$xyt$window,
  crop2parentwindow = TRUE,
  ...
)

Arguments

Value

an array, the [,,i]th slice being the grid of cell-wise autocorrelations.

betavals function

Description

A function to return the sampled beta from a call to the function lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars or lgcpPredictMultitypeSpatialPlusPars

Usage

betavals(lg)

Arguments

Value

the posterior sampled beta

See Also

ltar, autocorr, parautocorr, traceplots, parsummary, textsummary, priorpost, postcov, exceedProbs, etavals

blockcircbase function

Description

Compute the base matrix of a continuous Gaussian field. Computed as a block circulant matrix on a torus where x and y is the x and y centroids (must be equally spaced)

Usage

blockcircbase(x, y, sigma, phi, model, additionalparameters, inverse = FALSE)

Arguments

Value

the base matrix of a block circulant matrix representing a stationary covariance function on a toral grid.

blockcircbaseFunction function

Description

Compute the base matrix of a continuous Gaussian field. Computed as a block circulant matrix on a torus where x and y is the x and y centroids (must be equally spaced). This is an extension of the function blockcircbase to extend the range of covariance functions that can be fitted to the model.

Usage

blockcircbaseFunction(x, y, CovFunction, CovParameters, inverse = FALSE)

Arguments

Value

the base matrix of a block circulant matrix representing a stationary covariance function on a toral grid.

See Also

chooseCellwidth, getpolyol, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

bt.scalar function

Description

bt.scalar function

Usage

bt.scalar(t, theta)

Arguments

Value

...

checkObsWin function

Description

A function to run on an object generated by the "selectObsWindow" function. Plots the observation window with grid, use as a visual aid to check the choice of cell width is correct.

Usage

checkObsWin(ow)

Arguments

Value

a plot of the observation window and grid

See Also

chooseCellwidth

chooseCellwidth function

Description

A function to help choose the cell width (the parameter "cellwidth" in lgcpPredictSpatialPlusPars, for example) prior to setting up the FFT grid, before an MCMC run.

Usage

chooseCellwidth(obj, cwinit)

Arguments

Details

Ideally this function should be used after having made a preliminary guess at the parameters of the latent field.The idea is to run chooseCellwidth several times, adjusting the parameter "cwinit" so as to balance available computational resources with output grid size.

Value

produces a plot of the observation window and computational grid.

See Also

getpolyol, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

circulant function

Description

generic function for constructing circulant matrices

Usage

circulant(x, ...)

Arguments

Value

method circulant

circulant.matrix function

Description

If x is a matrix whose columns are the bases of the sub-blocks of a block circulant matrix, then this function returns the block circulant matrix of interest.

Usage

## S3 method for class 'matrix'
circulant(x, ...)

Arguments

Value

If x is a matrix whose columns are the bases of the sub-blocks of a block circulant matrix, then this function returns the block circulant matrix of interest.

circulant.numeric function

Description

returns a circulant matrix with base x

Usage

## S3 method for class 'numeric'
circulant(x, ...)

Arguments

Value

a circulant matrix with base x

clearinterp function

Description

A function to remove the interpolation methods from a data frame.

Usage

clearinterp(df)

Arguments

Value

removes the interpolation methods

computeGradtruncSpatial function

Description

Advanced use only. A function to compute a gradient truncation parameter for 'spatial only' MALA via simulation. The function requires an FFT 'grid' to be pre-computed, see fftgrid.

Usage

computeGradtruncSpatial(
  nsims = 100,
  scale = 1,
  nis,
  mu,
  rootQeigs,
  invrootQeigs,
  scaleconst,
  spatial,
  cellarea
)

Arguments

Value

gradient truncation parameter

See Also

fftgrid

computeGradtruncSpatioTemporal function

Description

Advanced use only. A function to compute a gradient truncation parameter for 'spatial only' MALA via simulation. The function requires an FFT 'grid' to be pre-computed, see fftgrid.

Usage

computeGradtruncSpatioTemporal(
  nsims = 100,
  scale = 1,
  nis,
  mu,
  rootQeigs,
  invrootQeigs,
  spatial,
  temporal,
  bt,
  cellarea
)

Arguments

Value

gradient truncation parameter

See Also

fftgrid

condProbs function

Description

A function to compute the conditional type-probabilities from a multivariate LGCP. See the vignette "Bayesian_lgcp" for a full explanation of this.

Usage

condProbs(obj)

Arguments

Details

We suppose there are K point types of interest. The model for point-type k is as follows:

X_k(s) ~ Poisson[R_k(s)]

R_k(s) = C_A lambda_k(s) exp[Z_k(s)beta_k+Y_k(s)]

Here X_k(s) is the number of events of type k in the computational grid cell containing the point s, R_k(s) is the Poisson rate, C_A is the cell area, lambda_k(s) is a known offset, Z_k(s) is a vector of measured covariates and Y_i(s) where i = 1,...,K+1 are latent Gaussian processes on the computational grid. The other parameters in the model are beta_k , the covariate effects for the kth type; and eta_i = [log(sigma_i),log(phi_i)], the parameters of the process Y_i for i = 1,...,K+1 on an appropriately transformed (again, in this case log) scale.

The term 'conditional probability of type k' means the probability that at a particular location there will be an event of type k, which denoted p_k.

Value

an lgcpgrid object containing the consitional type-probabilities for each type

See Also

segProbs, postcov.lgcpPredictSpatialOnlyPlusParameters, postcov.lgcpPredictAggregateSpatialPlusParameters, postcov.lgcpPredictSpatioTemporalPlusParameters, postcov.lgcpPredictMultitypeSpatialPlusParameters, ltar, autocorr, parautocorr, traceplots, parsummary, textsummary, priorpost, postcov, exceedProbs, betavals, etavals

constantInTime function

Description

Generic function for creating constant-in-time temporalAtRisk objects, that is for models where mu(t) can be assumed to be constant in time. The assumption being that the global at-risk population does not change in size over time.

Usage

constantInTime(obj, ...)

Arguments

Details

For further details of temporalAtRisk objects, see ?temporalAtRisk>

Value

method constantInTime

See Also

temporalAtRisk, spatialAtRisk, temporalAtRisk.numeric, temporalAtRisk.function, constantInTime.numeric, constantInTime.stppp, print.temporalAtRisk, plot.temporalAtRisk

constantInTime.numeric function

Description

Create a constant-in-time temporalAtRisk object from a numeric object of length 1. The returned temporalAtRisk object is assumed to have been scaled correctly by the user so that mu(t) = E(number of cases in a unit time interval).

Usage

## S3 method for class 'numeric'
constantInTime(obj, tlim, warn = TRUE, ...)

Arguments

Details

For further details of temporalAtRisk objects, see ?temporalAtRisk>

Value

a function f(t) giving the (constant) temporal intensity at time t for integer t in the interval [tlim[1],tlim[2]] of class temporalAtRisk

See Also

temporalAtRisk, spatialAtRisk, temporalAtRisk.numeric, temporalAtRisk.function, constantInTime, constantInTime.stppp, print.temporalAtRisk, plot.temporalAtRisk,

constantInTime.stppp function

Description

Create a constant-in-time temporalAtRisk object from an stppp object. The returned temporalAtRisk object is scaled to return mu(t) = E(number of cases in a unit time interval).

Usage

## S3 method for class 'stppp'
constantInTime(obj, ...)

Arguments

Details

For further details of temporalAtRisk objects, see ?temporalAtRisk>

Value

a function f(t) giving the (constant) temporal intensity at time t for integer t in the interval [tlim[1],tlim[2]] of class temporalAtRisk

See Also

temporalAtRisk, spatialAtRisk, temporalAtRisk.numeric, temporalAtRisk.function, constantInTime, constantInTime.numeric, print.temporalAtRisk, plot.temporalAtRisk,

constanth function

Description

This function is used to set up a constant acceptance scheme in the argument mcmc.control of the function lgcpPredict. The scheme is set via the mcmcpars function.

Usage

constanth(h)

Arguments

Value

object of class constanth

See Also

mcmcpars, lgcpPredict

Examples

constanth(0.01)

cov.interp.fft function

Description

A function to interpolate covariate values onto the fft grid, ready for analysis

Usage

cov.interp.fft(
  formula,
  W,
  regionalcovariates = NULL,
  pixelcovariates = NULL,
  mcens,
  ncens,
  cellInside,
  overl = NULL
)

Arguments

Value

The interpolated design matrix, ready for analysis

covEffects function

Description

A function used in conjunction with the function "expectation" to compute the main covariate effects,
lambda(s) exp[Z(s)beta]
in each computational grid cell. Currently only implemented for spatial processes (lgcpPredictSpatialPlusPars and lgcpPredictAggregateSpatialPlusPars).

Usage

covEffects(Y, beta, eta, Z, otherargs)

Arguments

Value

the main effects

See Also

expectation, lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars

Examples

## Not run: ex <- expectation(lg,covEffects)[[1]] # lg is output from spatial LGCP MCMC

d.func function

Description

d.func function

Usage

d.func(mat1il, mat2jk, i, j, l, k)

Arguments

Value

...

density.stppp function

Description

A wrapper function for density.ppp.

Usage

## S3 method for class 'stppp'
density(x, bandwidth = NULL, ...)

Arguments

Value

bivariate density estimate of xyt; not this is a wrapper function for density.ppp

See Also

density.ppp

discreteWindow function

Description

Generic function for extracting the FFT discrete window.

Usage

discreteWindow(obj, ...)

Arguments

Value

method discreteWindow

See Also

discreteWindow.lgcpPredict

discreteWindow.lgcpPredict function

Description

A function for extracting the FFT discrete window from an lgcpPredict object.

Usage

## S3 method for class 'lgcpPredict'
discreteWindow(obj, inclusion = "touching", ...)

Arguments

Value

...

dump2dir function

Description

This function, when set by the gridfunction argument of setoutput, in turn called by the argument output.control of lgcpPredict facilitates the dumping of data to disk. Data is dumped to a netCDF file, simout.nc, stored in the directory specified by the user. If the directory does not exist, then it will be created. Since the requested data dumped to disk may be very large in a run of lgcpPredict, by default, the user is prompted as to whether to proceed with prediction, this can be turned off by setting the option forceSave=TRUE detailed here. To save space, or increase the number of simulations that can be stored for a fixed disk space the option to only save the last time point is also available (lastonly=TRUE, which is the default setting).

Usage

dump2dir(dirname, lastonly = TRUE, forceSave = FALSE)

Arguments

Value

object of class dump2dir

See Also

setoutput, \ GFinitialise, GFupdate, GFfinalise, GFreturnvalue

eigenfrombase function

Description

A function to compute the eigenvalues of an SPD block circulant matrix given the base matrix.

Usage

eigenfrombase(x)

Arguments

Value

the eigenvalues

etavals function

Description

A function to return the sampled eta from a call to the function lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars or lgcpPredictMultitypeSpatialPlusPars

Usage

etavals(lg)

Arguments

Value

the posterior sampled eta

See Also

ltar, autocorr, parautocorr, traceplots, parsummary, textsummary, priorpost, postcov, exceedProbs, betavals

exceedProbs function

Description

This function can be called using MonteCarloAverage (see fun3 the examples in the help file for MonteCarloAverage). It computes exceedance probabilities,

P[\exp(Y_{t_1:t_2})>k],

that is the probability that the relative reisk exceeds threshold k. Note that it is possible to pass vectors of tresholds to the function, and the exceedance probabilities will be computed for each of these.

Usage

exceedProbs(threshold, direction = "upper")

Arguments

Value

a function of Y that computes the indicator function I(exp(Y)>threshold) evaluated for each cell of a matrix Y If several tresholds are specified an array is returned with the [,,i]th slice equal to I(exp(Y)>threshold[i])

See Also

MonteCarloAverage, setoutput

exceedProbsAggregated function

Description

NOTE THIS FUNCTION IS IN TESTING AT PRESENT

Usage

exceedProbsAggregated(threshold, lg = NULL, lastonly = TRUE)

Arguments

Details

This function computes regional exceedance probabilities after MCMC has finished, it requires the information to have been dumped to disk, and to have been computed using the function lgcpPredictAggregated

P[\exp(Y_{t_1:t_2})>k],

that is the probability that the relative risk exceeds threshold k. Note that it is possible to pass vectors of tresholds to the function, and the exceedance probabilities will be computed for each of these.

Value

a function of Y that computes the indicator function I(exp(Y)>threshold) evaluated for each cell of a matrix Y, but with values aggregated to regions If several tresholds are specified an array is returned with the [,,i]th slice equal to I(exp(Y)>threshold[i])

See Also

lgcpPredictAggregated

expectation function

Description

Generic function used in the computation of Monte Carlo expectations.

Usage

expectation(obj, ...)

Arguments

Value

method expectation

expectation.lgcpPredict function

Description

This function requires data to have been dumped to disk: see ?dump2dir and ?setoutput. This function computes the Monte Carlo Average of a function where data from a run of lgcpPredict has been dumped to disk.

Usage

## S3 method for class 'lgcpPredict'
expectation(obj, fun, maxit = NULL, ...)

Arguments

Details

A Monte Carlo Average is computed as:

E_{\pi(Y_{t_1:t_2}|X_{t_1:t_2})}[g(Y_{t_1:t_2})] \approx \frac1n\sum_{i=1}^n g(Y_{t_1:t_2}^{(i)})

where g is a function of interest, Y_{t_1:t_2}^{(i)} is the ith retained sample from the target and n is the total number of retained iterations. For example, to compute the mean of Y_{t_1:t_2} set,

g(Y_{t_1:t_2}) = Y_{t_1:t_2},

the output from such a Monte Carlo average would be a set of t_2-t_1 grids, each cell of which being equal to the mean over all retained iterations of the algorithm (NOTE: this is just an example computation, in practice, there is no need to compute the mean on line explicitly, as this is already done by default in lgcpPredict).

Value

the expectated value of that function

See Also

lgcpPredict, dump2dir, setoutput

expectation.lgcpPredictSpatialOnlyPlusParameters function

Description

This function requires data to have been dumped to disk: see ?dump2dir and ?setoutput. This function computes the Monte Carlo Average of a function where data from a run of lgcpPredict has been dumped to disk.

Usage

"expectation(obj,fun,maxit=NULL,...)"

Arguments

Value

the expectated value of that function

exponentialCovFct function

Description

A function to declare and also evaluate an exponential covariance function.

Usage

exponentialCovFct(d, CovParameters)

Arguments

Value

the exponential covariance function

See Also

CovFunction.function, RandomFieldsCovFct, SpikedExponentialCovFct

extendspatialAtRisk function

Description

A function to extend a spatialAtRisk object, used in interpolating the fft grid NOTE THIS DOES NOT RETURN A PROPER spatialAtRisk OBJECT SINCE THE NORMALISING CONSTANT IS PUT BACK IN.

Usage

extendspatialAtRisk(spatial)

Arguments

Value

the spatialAtRisk object on a slightly larger grid, with zeros appearing outside the original extent.

extract function

Description

Generic function for extracting information dumped to disk. See extract.lgcpPredict for further information.

Usage

extract(obj, ...)

Arguments

Value

method extract

See Also

extract.lgcpPredict

extract.lgcpPredict function

Description

This function requires data to have been dumped to disk: see ?dump2dir and ?setoutput. extract.lgcpPredict extracts chunks of data that have been dumped to disk. The subset of data can either be specified using an (x,y,t,s) box or (window,t,s) region where window is a polygonal subregion of interest.

Usage

## S3 method for class 'lgcpPredict'
extract(
  obj,
  x = NULL,
  y = NULL,
  t,
  s = -1,
  inWindow = NULL,
  crop2parentwindow = TRUE,
  ...
)

Arguments

Value

extracted array

See Also

lgcpPredict, loc2poly, dump2dir, setoutput

fftgrid function

Description

! As of lgcp version 0.9-5, this function is no longer used !

Usage

fftgrid(xyt, M, N, spatial, sigma, phi, model, covpars, inclusion = "touching")

Arguments

Details

Advanced use only. Computes various quantities for use in lgcpPredict, lgcpSim .

Value

fft objects for use in MALA

fftinterpolate function

Description

Generic function used for computing interpolations used in the function fftgrid.

Usage

fftinterpolate(spatial, ...)

Arguments

Value

method fftinterpolate

See Also

fftgrid

fftinterpolate.fromFunction function

Description

This method performs interpolation within the function fftgrid for fromFunction objects.

Usage

## S3 method for class 'fromFunction'
fftinterpolate(spatial, mcens, ncens, ext, ...)

Arguments

Value

matrix of interpolated values

See Also

fftgrid, spatialAtRisk.function

fftinterpolate.fromSPDF function

Description

This method performs interpolation within the function fftgrid for fromSPDF objects.

Usage

## S3 method for class 'fromSPDF'
fftinterpolate(spatial, mcens, ncens, ext, ...)

Arguments

Value

matrix of interpolated values

See Also

fftgrid, spatialAtRisk.SpatialPolygonsDataFrame

interpolate.fromXYZ function

Description

This method performs interpolation within the function fftgrid for fromXYZ objects.

Usage

## S3 method for class 'fromXYZ'
fftinterpolate(spatial, mcens, ncens, ext, ...)

Arguments

Value

matrix of interpolated values

See Also

fftgrid, spatialAtRisk.fromXYZ

fftmultiply function

Description

A function to pre-multiply a vector by a block cirulant matrix

Usage

fftmultiply(efb, vector)

Arguments

Value

a vector: the product of the matrix and the vector.

formulaList function

Description

A function to creat an object of class "formulaList" from a list of "formula" objects; use to define the model for the main effects prior to running the multivariate MCMC algorithm.

Usage

formulaList(X)

Arguments

Value

an object of class "formulaList"

gDisjoint_wg function

Description

A function to

Usage

gDisjoint_wg(w, gri)

Arguments

Value

...

gIntersects_pg function

Description

A function to

Usage

gIntersects_pg(spdf, grid)

Arguments

Value

...

gOverlay function

Description

A function to overlay the FFT grid, a SpatialPolygons object, onto a SpatialPolygonsDataFrame object.

Usage

gOverlay(grid, spdf)

Arguments

Details

this code was adapted from Roger Bivand:
https://stat.ethz.ch/pipermail/r-sig-geo/2011-June/012099.html

Value

a matrix describing the features of the overlay: the originating indices of grid and spdf (all non-trivial intersections) and the area of each intersection.

gTouches_wg function

Description

A function to

Usage

gTouches_wg(w, gri)

Arguments

Value

...

genFFTgrid function

Description

A function to generate an FFT grid and associated quantities including cell dimensions, size of extended grid, centroids, cell area, cellInside matrix (a 0/1 matrix: is the centroid of the cell inside the observation window?)

Usage

genFFTgrid(study.region, M, N, ext, inclusion = "touching")

Arguments

Value

a list

getCellCounts function

Description

This function is used to count the number of observations falling inside grid cells.

Usage

getCellCounts(x, y, xgrid, ygrid)

Arguments

Value

The number of observations in each grid cell.

getCounts function

Description

This function is used to count the number of observations falling inside grid cells, the output is used in the function lgcpPredict.

Usage

getCounts(xyt, subset = rep(TRUE, xyt$n), M, N, ext)

Arguments

Value

The number of observations in each grid cell returned on a grid suitable for use in the extended FFT space.

See Also

lgcpPredict

Examples

require(spatstat.explore)
xyt <- stppp(ppp(runif(100),runif(100)),t=1:100,tlim=c(1,100))
cts <- getCounts(xyt,M=64,N=64,ext=2) # gives an output grid of size 128 by 128
ctssub <- cts[1:64,1:64] # returns the cell counts in the observation
                         # window of interest

getCovParameters function

Description

Internal function for retrieving covariance parameters. not indended for general use.

Usage

getCovParameters(obj, ...)

Arguments

Value

method getCovParameters

getCovParameters.GPrealisation function

Description

Internal function for retrieving covariance parameters. not indended for general use.

Usage

## S3 method for class 'GPrealisation'
getCovParameters(obj, ...)

Arguments

Value

...

getCovParameters.list function

Description

Internal function for retrieving covariance parameters. not indended for general use.

Usage

## S3 method for class 'list'
getCovParameters(obj, ...)

Arguments

Value

...

getLHSformulaList function

Description

A function to retrieve the dependent variables from a formulaList object. Not intended for general use.

Usage

getLHSformulaList(fl)

Arguments

Value

the indepentdent variables

getRotation function

Description

Generic function for the computation of rotation matrices.

Usage

getRotation(xyt, ...)

Arguments

Value

method getRotation

See Also

getRotation.stppp

getRotation.default function

Description

Presently there is no default method, see ?getRotation.stppp

Usage

## Default S3 method:
getRotation(xyt, ...)

Arguments

Value

currently no default implementation

See Also

getRotation.stppp

getRotation.stppp function

Description

Compute rotation matrix if observation window is a polygonal boundary

Usage

## S3 method for class 'stppp'
getRotation(xyt, ...)

Arguments

Value

the optimal rotation matrix and rotated data and observation window. Note it may or may not be advantageous to rotate the window, this information is displayed prior to the MALA routine when using lgcpPredict

getZmat function

Description

A function to construct a design matrix for use with the Bayesian MCMC routines in lgcp. See the vignette "Bayesian_lgcp" for further details on how to use this function.

Usage

getZmat(
  formula,
  data,
  regionalcovariates = NULL,
  pixelcovariates = NULL,
  cellwidth,
  ext = 2,
  inclusion = "touching",
  overl = NULL
)

Arguments

Details

For example, a spatial LGCP model for the would have the form:

X(s) ~ Poisson[R(s)]

R(s) = C_A lambda(s) exp[Z(s)beta+Y(s)]

The function getZmat helps create the matrix Z. The returned object is passed onto an MCMC function, for example lgcpPredictSpatialPlusPars or lgcpPredictAggregateSpatialPlusPars. This function can also be used to help construct Z for use with lgcpPredictSpatioTemporalPlusPars and lgcpPredictMultitypeSpatialPlusPars, but these functions require a list of such objects: see the vignette "Bayesian_lgcp" for examples.

Value

a design matrix for passing on to the Bayesian MCMC functions

See Also

chooseCellwidth, getpolyol, guessinterp, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

getZmats function

Description

An internal function to create Z_k from an lgcpZmat object, for use in the multivariate MCMC algorithm. Not intended for general use.

Usage

getZmats(Zmat, formulaList)

Arguments

Value

design matrices for each of the point types

getinterp function

Description

A function to get the interpolation methods from a data frame

Usage

getinterp(df)

Arguments

Details

The three types of interpolation method employed in the package lgcp are:

1. 'Majority' The interpolated value corresponds to the value of the covariate occupying the largest area of the computational cell.

2. 'ArealWeightedMean' The interpolated value corresponds to the mean of all covariate values contributing to the computational cell weighted by their respective areas.

3. 'ArealWeightedSum' The interpolated value is the sum of all contributing covariates weighed by the proportion of area with respect to the covariate polygons. For example, suppose region A has the same area as a computational grid cell and has 500 inhabitants. If that region occupies half of a computational grid cell, then this interpolation type assigns 250 inhabitants from A to the computational grid cell.

Value

the interpolation methods

getlgcpPredictSpatialINLA function

Description

A function to download and 'install' lgcpPredictSpatialINLA into the lgcp namespace.

Usage

getlgcpPredictSpatialINLA()

Value

Does not return anything

getpolyol function

Description

A function to perform polygon/polygon overlay operations and form the computational grid, on which inference will eventually take place. For details and examples of using this fucntion, please see the package vignette "Bayesian_lgcp"

Usage

getpolyol(
  data,
  regionalcovariates = NULL,
  pixelcovariates = NULL,
  cellwidth,
  ext = 2,
  inclusion = "touching"
)

Arguments

Value

an object of class lgcppolyol, which can then be fed into the function getZmat.

See Also

chooseCellwidth, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

getup function

Description

A function to get an object from a parent frame.

Usage

getup(n, lev = 1)

Arguments

Value

...

ginhomAverage function

Description

A function to estimate the inhomogeneous pair correlation function for a spatiotemporal point process. See equation (8) of Diggle P, Rowlingson B, Su T (2005).

Usage

ginhomAverage(
  xyt,
  spatial.intensity,
  temporal.intensity,
  time.window = xyt$tlim,
  rvals = NULL,
  correction = "iso",
  suppresswarnings = FALSE,
  ...
)

Arguments

Value

time average of inhomogenous pcf, equation (13) of Brix and Diggle 2001.

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Baddeley AJ, Moller J, Waagepetersen R (2000). Non-and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54, 329-350.

3. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

4. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

See Also

KinhomAverage, spatialparsEst, thetaEst, lambdaEst, muEst

grid2spdf function

Description

A function to convert a regular (x,y) grid of centroids into a SpatialPoints object

Usage

grid2spdf(xgrid, ygrid, proj4string = CRS(as.character(NA)))

Arguments

Value

a SpatialPolygonsDataFrame

grid2spix function

Description

A function to convert a regular (x,y) grid of centroids into a SpatialPixels object

Usage

grid2spix(xgrid, ygrid, proj4string = CRS(as.character(NA)))

Arguments

Value

a SpatialPixels object

grid2spoly function

Description

A function to convert a regular (x,y) grid of centroids into a SpatialPolygons object

Usage

grid2spoly(xgrid, ygrid, proj4string = CRS(as.character(NA)))

Arguments

Value

a SpatialPolygons object

grid2spts function

Description

A function to convert a regular (x,y) grid of centroids into a SpatialPoints object

Usage

grid2spts(xgrid, ygrid, proj4string = CRS(as.character(NA)))

Arguments

Value

a SpatialPoints object

gridInWindow function

Description

For the grid defined by x-coordinates, xvals, and y-coordinates, yvals, and an owin object W, this function just returns a logical matrix M, whose [i,j] entry is TRUE if the point(xvals[i], yvals[j]) is inside the observation window.

Usage

gridInWindow(xvals, yvals, win, inclusion = "touching")

Arguments

Value

matrix of TRUE/FALSE, which elements of the grid are inside the observation window win

gridav function

Description

A generic function for returning gridmeans objects.

Usage

gridav(obj, ...)

Arguments

Value

method gridav

See Also

setoutput, lgcpgrid

gridav.lgcpPredict function

Description

Accessor function for lgcpPredict objects: returns the gridmeans argument set in the output.control argument of the function lgcpPredict.

Usage

## S3 method for class 'lgcpPredict'
gridav(obj, fun = NULL, ...)

Arguments

Value

returns the output from the gridmeans option of the setoutput argument of lgcpPredict

See Also

setoutput, lgcpgrid

gridfun function

Description

A generic function for returning gridfunction objects.

Usage

gridfun(obj, ...)

Arguments

Value

method gridfun

See Also

setoutput, lgcpgrid

gridfun.lgcpPredict function

Description

Accessor function for lgcpPredict objects: returns the gridfunction argument set in the output.control argument of the function lgcpPredict.

Usage

## S3 method for class 'lgcpPredict'
gridfun(obj, ...)

Arguments

Value

returns the output from the gridfunction option of the setoutput argument of lgcpPredict

See Also

setoutput, lgcpgrid

gu function

Description

gu function

Usage

gu(u, sigma, phi, model, additionalparameters)

Arguments

Value

this is just a wrapper for CovarianceFct

guessinterp function

Description

A function to guess provisional interpolational methods to variables in a data frame. Numeric variables are assigned interpolation by areal weighted mean (see below); factor, character and other types of variable are assigned interpolation by majority vote (see below). Not that the interpolation type ArealWeightedSum is not assigned automatically.

Usage

guessinterp(df)

Arguments

Details

The three types of interpolation method employed in the package lgcp are:

1. 'Majority' The interpolated value corresponds to the value of the covariate occupying the largest area of the computational cell.

2. 'ArealWeightedMean' The interpolated value corresponds to the mean of all covariate values contributing to the computational cell weighted by their respective areas.

3. 'ArealWeightedSum' The interpolated value is the sum of all contributing covariates weighed by the proportion of area with respect to the covariate polygons. For example, suppose region A has the same area as a computational grid cell and has 500 inhabitants. If that region occupies half of a computational grid cell, then this interpolation type assigns 250 inhabitants from A to the computational grid cell.

Value

the data frame, but with attributes describing the interpolation method for each variable

See Also

chooseCellwidth, getpolyol, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

Examples

## Not run: spdf a SpatialPolygonsDataFrame
## Not run: spdf@data <- guessinterp(spdf@data)

generic hasNext method

Description

test if an iterator has any more values to go

Usage

hasNext(obj)

Arguments

hasNext.iter function

Description

method for iter objects test if an iterator has any more values to go

Usage

## S3 method for class 'iter'
hasNext(obj)

Arguments

hvals function

Description

Generic function to return the values of the proposal scaling h in the MCMC algorithm.

Usage

hvals(obj, ...)

Arguments

Value

method hvals

hvals.lgcpPredict function

Description

Accessor function returning the value of h, the MALA proposal scaling constant over the iterations of the algorithm for objects of class lgcpPredict

Usage

## S3 method for class 'lgcpPredict'
hvals(obj, ...)

Arguments

Value

returns the values of h taken during the progress of the algorithm

See Also

lgcpPredict

identify.lgcpPredict function

Description

Identifies the indices of grid cells on plots of lgcpPredict objects. Can be used to identify a small number of cells for further information eg trace or autocorrelation plots (provided data has been dumped to disk). On calling identify(lg) for example (see code below), the user can click multiply with the left mouse button on the graphics device; once the user has selected all points of interest, the right button is pressed, which returns them.

Usage

## S3 method for class 'lgcpPredict'
identify(x, ...)

Arguments

Value

a 2 x n matrix containing the grid indices of the points of interest, where n is the number of points selected via the mouse.

See Also

lgcpPredict, loc2poly

Examples

## Not run: plot(lg) # lg an lgcpPredict object
## Not run: pt_indices <- identify(lg)

identifygrid function

Description

Identifies the indices of grid cells on plots of objects.

Usage

identifygrid(x, y)

Arguments

Value

a 2 x n matrix containing the grid indices of the points of interest, where n is the number of points selected via the mouse.

See Also

lgcpPredict, loc2poly, identify.lgcpPredict

image.lgcpgrid function

Description

Produce an image plot of an lgcpgrid object.

Usage

## S3 method for class 'lgcpgrid'
image(x, sel = 1:x$len, ask = TRUE, ...)

Arguments

Value

grid plotting

See Also

lgcpgrid.list, lgcpgrid.array, as.list.lgcpgrid, print.lgcpgrid, summary.lgcpgrid, quantile.lgcpgrid, plot.lgcpgrid

initialiseAMCMC function

Description

A generic to be used for the purpose of user-defined adaptive MCMC schemes, initialiseAMCMC tells the MALA algorithm which value of h to use first. See lgcp vignette, codevignette("lgcp"), for further details on writing adaptive MCMC schemes.

Usage

initialiseAMCMC(obj, ...)

Arguments

Value

method intialiseAMCMC

See Also

initialiseAMCMC.constanth, initialiseAMCMC.andrieuthomsh

initaliseAMCMC.andrieuthomsh function

Description

Initialises the andrieuthomsh adaptive scheme.

Usage

## S3 method for class 'andrieuthomsh'
initialiseAMCMC(obj, ...)

Arguments

Value

initial h for scheme

References

1. Andrieu C, Thoms J (2008). A tutorial on adaptive MCMC. Statistics and Computing, 18(4), 343-373.

2. Robbins H, Munro S (1951). A Stochastic Approximation Methods. The Annals of Mathematical Statistics, 22(3), 400-407.

3. Roberts G, Rosenthal J (2001). Optimal Scaling for Various Metropolis-Hastings Algorithms. Statistical Science, 16(4), 351-367.

See Also

andrieuthomsh

initaliseAMCMC.constanth function

Description

Initialises the constanth adaptive scheme.

Usage

## S3 method for class 'constanth'
initialiseAMCMC(obj, ...)

Arguments

Value

initial h for scheme

See Also

constanth

integerise function

Description

Generic function for converting the time variable of an stppp object.

Usage

integerise(obj, ...)

Arguments

Value

method integerise

See Also

integerise.stppp

integerise.mstppp function

Description

Function for converting the times and time limits of an mstppp object into integer values.

Usage

## S3 method for class 'mstppp'
integerise(obj, ...)

Arguments

Value

The mstppp object, but with integerised times.

integerise.stppp function

Description

Function for converting the times and time limits of an stppp object into integer values. Do this before estimating mu(t), and hence before creating the temporalAtRisk object. Not taking this step is possible in lgcp, but can cause minor complications connected with the scaling of mu(t).

Usage

## S3 method for class 'stppp'
integerise(obj, ...)

Arguments

Value

The stppp object, but with integerised times.

intens function

Description

Generic function to return the Poisson Intensity.

Usage

intens(obj, ...)

Arguments

Value

method intens

See Also

lgcpPredict, intens.lgcpPredict

intens.lgcpPredict function

Description

Accessor function returning the Poisson intensity as an lgcpgrid object.

Usage

## S3 method for class 'lgcpPredict'
intens(obj, ...)

Arguments

Value

the cell-wise mean Poisson intensity, as computed by MCMC.

See Also

lgcpPredict

intens.lgcpSimMultitypeSpatialPlusParameters function

Description

A function to return the cellwise Poisson intensity used during in constructing the simulated data.

Usage

"intens(obj, ...)"

Arguments

Value

the Poisson intensity

intens.lgcpSimSpatialPlusParameters function

Description

A function to return the cellwise Poisson intensity used during in constructing the simulated data.

Usage

## S3 method for class 'lgcpSimSpatialPlusParameters'
intens(obj, ...)

Arguments

Value

the Poisson intensity

interptypes function

Description

A function to return the types of covariate interpolation available

Usage

interptypes()

Details

The three types of interpolation method employed in the package lgcp are:

1. 'Majority' The interpolated value corresponds to the value of the covariate occupying the largest area of the computational cell.

2. 'ArealWeightedMean' The interpolated value corresponds to the mean of all covariate values contributing to the computational cell weighted by their respective areas.

3. 'ArealWeightedSum' The interpolated value is the sum of all contributing covariates weighed by the proportion of area with respect to the covariate polygons. For example, suppose region A has the same area as a computational grid cell and has 500 inhabitants. If that region occupies half of a computational grid cell, then this interpolation type assigns 250 inhabitants from A to the computational grid cell.

Value

character string of available interpolation types

inversebase function

Description

A function to compute the base of the inverse os a block circulant matrix, given the base of the matrix

Usage

inversebase(x)

Arguments

Value

the base matrix of the inverse of the circulant matrix

is.SPD function

Description

A function to compute whether a block circulant matrix is symmetric positive definite (SPD), given its base matrix.

Usage

is.SPD(base)

Arguments

Value

logical, whether the circulant matrix the base represents is SPD

is this a burn-in iteration?

Description

if this mcmc iteration is in the burn-in period, return TRUE

Usage

is.burnin(obj)

Arguments

Value

TRUE or FALSE

is.pow2 function

Description

Tests whether a number id

Usage

is.pow2(num)

Arguments

Value

logical: is num a power of 2?

Examples

is.pow2(128)  # TRUE
is.pow2(64.9) # FALSE

do we retain this iteration?

Description

if this mcmc iteration is one not thinned out, this is true

Usage

is.retain(obj)

Arguments

Value

TRUE or FALSE

iteration number

Description

within a loop, this is the iteration number we are currently doing.

Usage

iteration(obj)

Arguments

Details

get the iteration number

Value

integer iteration number, starting from 1.

lambdaEst function

Description

Generic function for estimating bivariate densities by eye. Specific methods exist for stppp objects and ppp objects.

Usage

lambdaEst(xyt, ...)

Arguments

Value

method lambdaEst

See Also

lambdaEst.stppp, lambdaEst.ppp

lambdaEst.ppp function

Description

A tool for the visual estimation of lambda(s) via a 2 dimensional smoothing of the case locations. For parameter estimation, the alternative is to estimate lambda(s) by some other means, convert it into a spatialAtRisk object and then into a pixel image object using the build in coercion methods, this im object can then be fed to ginhomAverage, KinhomAverage or thetaEst for instance.

Usage

## S3 method for class 'ppp'
lambdaEst(xyt, weights = c(), edge = TRUE, bw = NULL, ...)

Arguments

Details

The function lambdaEst is built directly on the density.ppp function and as such, implements a bivariate Gaussian smoothing kernel. The bandwidth is initially that which is automatically chosen by the default method of density.ppp. Since image plots of these kernel density estimates may not have appropriate colour scales, the ability to adjust this is given with the slider 'colour adjustment'. With colour adjustment set to 1, the default image.plot for the equivalent pixel image object is shown and for values less than 1, the colour scheme is more spread out, allowing the user to get a better feel for the density that is being fitted. NOTE: colour adjustment does not affect the returned density and the user should be aware that the returned density will 'look like' that displayed when colour adjustment is set equal to 1.

Value

This is an rpanel function for visual choice of lambda(s), the output is a variable, varname, with the density *per unit time* the variable varname can be fed to the function ginhomAverage or KinhomAverage as the argument density (see for example ?ginhomAverage), or into the function thetaEst as the argument spatial.intensity.

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

3. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

See Also

spatialAtRisk, ginhomAverage, KinhomAverage, spatialparsEst, thetaEst, muEst

lambdaEst.stppp function

Description

A tool for the visual estimation of lambda(s) via a 2 dimensional smoothing of the case locations. For parameter estimation, the alternative is to estimate lambda(s) by some other means, convert it into a spatialAtRisk object and then into a pixel image object using the build in coercion methods, this im object can then be fed to ginhomAverage, KinhomAverage or thetaEst for instance.

Usage

## S3 method for class 'stppp'
lambdaEst(xyt, weights = c(), edge = TRUE, bw = NULL, ...)

Arguments

Details

The function lambdaEst is built directly on the density.ppp function and as such, implements a bivariate Gaussian smoothing kernel. The bandwidth is initially that which is automatically chosen by the default method of density.ppp. Since image plots of these kernel density estimates may not have appropriate colour scales, the ability to adjust this is given with the slider 'colour adjustment'. With colour adjustment set to 1, the default image.plot for the equivalent pixel image object is shown and for values less than 1, the colour scheme is more spread out, allowing the user to get a better feel for the density that is being fitted. NOTE: colour adjustment does not affect the returned density and the user should be aware that the returned density will 'look like' that displayed when colour adjustment is set equal to 1.

Value

This is an rpanel function for visual choice of lambda(s), the output is a variable, varname, with the density *per unit time* the variable varname can be fed to the function ginhomAverage or KinhomAverage as the argument density (see for example ?ginhomAverage), or into the function thetaEst as the argument spatial.intensity.

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

3. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

See Also

spatialAtRisk, ginhomAverage, KinhomAverage, spatialparsEst, thetaEst, muEst

lgcpForecast function

Description

Function to produce forecasts for the mean field Y at times beyond the last time point in the analysis (given by the argument T in the function lgcpPredict).

Usage

lgcpForecast(
  lg,
  ptimes,
  spatial.intensity,
  temporal.intensity,
  inclusion = "touching"
)

Arguments

Value

forcasted relative risk, Poisson intensities and Y values over grid, together with approximate variance.

References

Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

See Also

lgcpPredict

lgcpInits function

Description

A function to declare initial values for a run of the MCMC routine. If specified, the MCMC algorithm will calibrate the proposal density using these as provisional estimates of the parameters.

Usage

lgcpInits(etainit = NULL, betainit = NULL)

Arguments

Details

It is not necessary to supply intial values to the MCMC routine, by default the functions lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars and lgcpPredictMultitypeSpatialPlusPars will initialise the MCMC as follows. For eta, if no initial value is specified then the initial value of eta in the MCMC run will be the prior mean. For beta, if no initial value is specified then the initial value of beta in the MCMC run will be estimated from an overdispersed Poisson fit to the cell counts, ignoring spatial correlation. The user cannot specify an initial value of Y (or equivalently Gamma), as a sensible value is chosen by the MCMC function.

A secondary function of specifying initial values is to help design the MCMC proposal matrix, which is based on these initial estimates.

Value

an object of class lgcpInits used in the MCMC routine.

See Also

chooseCellwidth, getpolyol, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, CovFunction, lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars

Examples

## Not run: INITS <- lgcpInits(etainit=log(c(sqrt(1.5),275)), betainit=NULL)

lgcpPredict function

Description

The function lgcpPredict performs spatiotemporal prediction for log-Gaussian Cox Processes

Usage

lgcpPredict(
  xyt,
  T,
  laglength,
  model.parameters = lgcppars(),
  spatial.covmodel = "exponential",
  covpars = c(),
  cellwidth = NULL,
  gridsize = NULL,
  spatial.intensity,
  temporal.intensity,
  mcmc.control,
  output.control = setoutput(),
  missing.data.areas = NULL,
  autorotate = FALSE,
  gradtrunc = Inf,
  ext = 2,
  inclusion = "touching"
)

Arguments

Details

The following is a mathematical description of a log-Gaussian Cox Process, it is best viewed in the pdf version of the manual.

Let \mathcal Y(s,t) be a spatiotemporal Gaussian process, W\subset R^2 be an observation window in space and T\subset R_{\geq 0} be an interval of time of interest. Cases occur at spatio-temporal positions (x,t) \in W \times T according to an inhomogeneous spatio-temporal Cox process, i.e. a Poisson process with a stochastic intensity R(x,t), The number of cases, X_{S,[t_1,t_2]}, arising in any S \subseteq W during the interval [t_1,t_2]\subseteq T is then Poisson distributed conditional on R(\cdot),

X_{S,[t_1,t_2]} \sim \mbox{Poisson}\left\{\int_S\int_{t_1}^{t_2} R(s,t)d sd t\right\}

Following Brix and Diggle (2001) and Diggle et al (2005), the intensity is decomposed multiplicatively as

R(s,t) = \lambda(s)\mu(t)\exp\{\mathcal Y(s,t)\}.

In the above, the fixed spatial component, \lambda:R^2\mapsto R_{\geq 0}, is a known function, proportional to the population at risk at each point in space and scaled so that

\int_W\lambda(s)d s=1,

whilst the fixed temporal component, \mu:R_{\geq 0}\mapsto R_{\geq 0}, is also a known function with

\mu(t) \delta t = E[X_{W,\delta t}],

for t in a small interval of time, \delta t, over which the rate of the process over W can be considered constant.

NOTE: the xyt stppp object can be recorded in continuous time, but for the purposes of prediciton, discretisation must take place. For the time dimension, this is achieved invisibly by as.integer(xyt$t) and as.integer(xyt$tlim). Therefore, before running an analysis please make sure that this is commensurate with the physical inerpretation and requirements of your output. The spatial discretisation is chosen with the argument cellwidth (or gridsize). If the chosen discretisation in time and space is too coarse for a given set of parameters (sigma, phi and theta) then the proper correlation structures implied by the model will not be captured in the output.

Before calling this function, the user must decide on the time point of interest, the number of intervals of data to use, the parameters, spatial covariance model, spatial discretisation, fixed spatial (\lambda(s)) and temporal (\mu(t)) components, mcmc parameters, and whether or not any output is required.

Value

the results of fitting the model in an object of class lgcpPredict

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

3. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

4. Wood ATA, Chan G (1994). Simulation of Stationary Gaussian Processes in [0,1]d. Journal of Computational and Graphical Statistics, 3(4), 409-432.

5. Moller J, Syversveen AR, Waagepetersen RP (1998). Log Gaussian Cox Processes. Scandinavian Journal of Statistics, 25(3), 451-482.

See Also

KinhomAverage, ginhomAverage, lambdaEst, muEst, spatialparsEst, thetaEst, spatialAtRisk, temporalAtRisk, lgcppars, CovarianceFct, mcmcpars, setoutput print.lgcpPredict, xvals.lgcpPredict, yvals.lgcpPredict, plot.lgcpPredict, meanfield.lgcpPredict, rr.lgcpPredict, serr.lgcpPredict, intens.lgcpPredict, varfield.lgcpPredict, gridfun.lgcpPredict, gridav.lgcpPredict, hvals.lgcpPredict, window.lgcpPredict, mcmctrace.lgcpPredict, plotExceed.lgcpPredict, quantile.lgcpPredict, identify.lgcpPredict, expectation.lgcpPredict, extract.lgcpPredict, showGrid.lgcpPredict

lgcpPredictAggregateSpatialPlusPars function

Description

A function to deliver fully Bayesian inference for the aggregated spatial log-Gaussian Cox process.

Usage

lgcpPredictAggregateSpatialPlusPars(
  formula,
  spdf,
  Zmat = NULL,
  overlayInZmat = FALSE,
  model.priors,
  model.inits = lgcpInits(),
  spatial.covmodel,
  cellwidth = NULL,
  poisson.offset = NULL,
  mcmc.control,
  output.control = setoutput(),
  gradtrunc = Inf,
  ext = 2,
  Nfreq = 101,
  inclusion = "touching",
  overlapping = FALSE,
  pixwts = NULL
)

Arguments

Details

See the vignette "Bayesian_lgcp" for examples of this code in use.

In this case, we OBSERVE case counts in the regions of a SpatialPolygonsDataFrame; the counts are stored as a variable, X. The model for the UNOBSERVED data, X(s), is as follows:

X(s) ~ Poisson[R(s)]

R(s) = C_A lambda(s) exp[Z(s)beta+Y(s)]

Here X(s) is the number of events in the cell of the computational grid containing s, R(s) is the Poisson rate, C_A is the cell area, lambda(s) is a known offset, Z(s) is a vector of measured covariates and Y(s) is the latent Gaussian process on the computational grid. The other parameters in the model are beta, the covariate effects; and eta=[log(sigma),log(phi)], the parameters of the process Y on an appropriately transformed (in this case log) scale.

We recommend the user takes the following steps before running this method:

1. Compute approximate values of the parameters, eta, of the process Y using the function minimum.contrast. These approximate values are used for two main reasons: (1) to help inform the size of the computational grid, since we will need to use a cell width that enables us to capture the dependence properties of Y and (2) to help inform the proposal kernel for the MCMC algorithm.

2. Choose an appropriate grid on which to perform inference using the function chooseCellwidth; this will partly be determined by the results of the first stage and partly by the available computational resource available to perform inference.

3. Using the function getpolyol, construct the computational grid and polygon overlays, as required. As this can be an expensive step, we recommend that the user saves this object after it has been constructed and in future reference to the data, reloads this object, rather than having to re-compute it (provided the computational grid has not changed).

4. Decide on which covariates are to play a part in the analysis and use the lgcp function getZmat to interpolate these onto the computational grid. Note that having saved the results from the previous step, this is a relatively quick operation, and allows the user to quickly construct different design matrices, Z, from different candidate models for the data

5. If required, set up the population offset using SpatialAtRisk functions (see the vignette "Bayesian_lgcp"); specify the priors using lgcpPrior; and if desired, the initial values for the MCMC, using the function lgcpInits.

6. Run the MCMC algorithm and save the output to disk. We recommend dumping information to disk using the dump2dir function in the output.control argument because it offers much greater flexibility in terms of MCMC diagnosis and post-processing.

7. Perform post-processing analyses including MCMC diagnostic checks and produce summaries of the posterior expectations we require for presentation. (see the vignette "Bayesian_lgcp" for further details). Functions of use in this step include traceplots, autocorr, parautocorr, ltar, parsummary, priorpost, postcov, textsummary, expectation, exceedProbs and lgcp:::expectation.lgcpPredict

Value

an object of class lgcpPredictAggregateSpatialPlusParameters

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle. Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R. Submitted.

2. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

3. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

4. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

5. Wood ATA, Chan G (1994). Simulation of Stationary Gaussian Processes in [0,1]d. Journal of Computational and Graphical Statistics, 3(4), 409-432.

6. Moller J, Syversveen AR, Waagepetersen RP (1998). Log Gaussian Cox Processes. Scandinavian Journal of Statistics, 25(3), 451-482.

See Also

linkchooseCellWidth, getpolyol, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, lgcpPredictMultitypeSpatialPlusPars, ltar, autocorr, parautocorr, traceplots, parsummary, textsummary, priorpost, postcov, exceedProbs, betavals, etavals

lgcpPredictAggregated function

Description

The function lgcpPredict performs spatiotemporal prediction for log-Gaussian Cox Processes for point process data where counts have been aggregated to the regional level. This is achieved by imputation of the regional counts onto a spatial continuum; if something is known about the underlying spatial density of cases, then this information can be added to improve the quality of the imputation, without this, the counts are distributed uniformly within regions.

Usage

lgcpPredictAggregated(
  app,
  popden = NULL,
  T,
  laglength,
  model.parameters = lgcppars(),
  spatial.covmodel = "exponential",
  covpars = c(),
  cellwidth = NULL,
  gridsize = NULL,
  spatial.intensity,
  temporal.intensity,
  mcmc.control,
  output.control = setoutput(),
  autorotate = FALSE,
  gradtrunc = NULL,
  n = 100,
  dmin = 0,
  check = TRUE
)

Arguments

Details

The following is a mathematical description of a log-Gaussian Cox Process, it is best viewed in the pdf version of the manual.

Let \mathcal Y(s,t) be a spatiotemporal Gaussian process, W\subset R^2 be an observation window in space and T\subset R_{\geq 0} be an interval of time of interest. Cases occur at spatio-temporal positions (x,t) \in W \times T according to an inhomogeneous spatio-temporal Cox process, i.e. a Poisson process with a stochastic intensity R(x,t), The number of cases, X_{S,[t_1,t_2]}, arising in any S \subseteq W during the interval [t_1,t_2]\subseteq T is then Poisson distributed conditional on R(\cdot),

X_{S,[t_1,t_2]} \sim \mbox{Poisson}\left\{\int_S\int_{t_1}^{t_2} R(s,t)d sd t\right\}

Following Brix and Diggle (2001) and Diggle et al (2005), the intensity is decomposed multiplicatively as

R(s,t) = \lambda(s)\mu(t)\exp\{\mathcal Y(s,t)\}.

In the above, the fixed spatial component, \lambda:R^2\mapsto R_{\geq 0}, is a known function, proportional to the population at risk at each point in space and scaled so that

\int_W\lambda(s)d s=1,

whilst the fixed temporal component, \mu:R_{\geq 0}\mapsto R_{\geq 0}, is also a known function with

\mu(t) \delta t = E[X_{W,\delta t}],

for t in a small interval of time, \delta t, over which the rate of the process over W can be considered constant.

NOTE: the xyt stppp object can be recorded in continuous time, but for the purposes of prediciton, discretisation must take place. For the time dimension, this is achieved invisibly by as.integer(xyt$t) and as.integer(xyt$tlim). Therefore, before running an analysis please make sure that this is commensurate with the physical inerpretation and requirements of your output. The spatial discretisation is chosen with the argument cellwidth (or gridsize). If the chosen discretisation in time and space is too coarse for a given set of parameters (sigma, phi and theta) then the proper correlation structures implied by the model will not be captured in the output.

Before calling this function, the user must decide on the time point of interest, the number of intervals of data to use, the parameters, spatial covariance model, spatial discretisation, fixed spatial (\lambda(s)) and temporal (\mu(t)) components, mcmc parameters, and whether or not any output is required.

Value

the results of fitting the model in an object of class lgcpPredict

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

3. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

4. Wood ATA, Chan G (1994). Simulation of Stationary Gaussian Processes in [0,1]d. Journal of Computational and Graphical Statistics, 3(4), 409-432.

5. Moller J, Syversveen AR, Waagepetersen RP (1998). Log Gaussian Cox Processes. Scandinavian Journal of Statistics, 25(3), 451-482.

See Also

KinhomAverage, ginhomAverage, lambdaEst, muEst, spatialparsEst, thetaEst, spatialAtRisk, temporalAtRisk, lgcppars, CovarianceFct, mcmcpars, setoutput print.lgcpPredict, xvals.lgcpPredict, yvals.lgcpPredict, plot.lgcpPredict, meanfield.lgcpPredict, rr.lgcpPredict, serr.lgcpPredict, intens.lgcpPredict, varfield.lgcpPredict, gridfun.lgcpPredict, gridav.lgcpPredict, hvals.lgcpPredict, window.lgcpPredict, mcmctrace.lgcpPredict, plotExceed.lgcpPredict, quantile.lgcpPredict, identify.lgcpPredict, expectation.lgcpPredict, extract.lgcpPredict, showGrid.lgcpPredict

lgcpPredictMultitypeSpatialPlusPars function

Description

A function to deliver fully Bayesian inference for a multitype spatial log-Gaussian Cox process.

Usage

lgcpPredictMultitypeSpatialPlusPars(
  formulaList,
  sd,
  typemark = NULL,
  Zmat = NULL,
  model.priorsList,
  model.initsList = NULL,
  spatial.covmodelList,
  cellwidth = NULL,
  poisson.offset = NULL,
  mcmc.control,
  output.control = setoutput(),
  gradtrunc = Inf,
  ext = 2,
  inclusion = "touching"
)

Arguments

Details

See the vignette "Bayesian_lgcp" for examples of this code in use.

We suppose there are K point types of interest. The model for point-type k is as follows:

X_k(s) ~ Poisson[R_k(s)]

R_k(s) = C_A lambda_k(s) exp[Z_k(s)beta_k+Y_k(s)]

Here X_k(s) is the number of events of type k in the computational grid cell containing the point s, R_k(s) is the Poisson rate, C_A is the cell area, lambda_k(s) is a known offset, Z_k(s) is a vector of measured covariates and Y_i(s) where i = 1,...,K+1 are latent Gaussian processes on the computational grid. The other parameters in the model are beta_k , the covariate effects for the kth type; and eta_i = [log(sigma_i),log(phi_i)], the parameters of the process Y_i for i = 1,...,K+1 on an appropriately transformed (again, in this case log) scale.

We recommend the user takes the following steps before running this method:

1. Compute approximate values of the parameters, eta, of the process Y using the function minimum.contrast. These approximate values are used for two main reasons: (1) to help inform the size of the computational grid, since we will need to use a cell width that enables us to capture the dependence properties of Y and (2) to help inform the proposal kernel for the MCMC algorithm.

2. Choose an appropriate grid on which to perform inference using the function chooseCellwidth; this will partly be determined by the results of the first stage and partly by the available computational resource available to perform inference.

3. Using the function getpolyol, construct the computational grid and polygon overlays, as required. As this can be an expensive step, we recommend that the user saves this object after it has been constructed and in future reference to the data, reloads this object, rather than having to re-compute it (provided the computational grid has not changed).

4. Decide on which covariates are to play a part in the analysis and use the lgcp function getZmat to interpolate these onto the computational grid. Note that having saved the results from the previous step, this is a relatively quick operation, and allows the user to quickly construct different design matrices, Z, from different candidate models for the data

5. If required, set up the population offset using SpatialAtRisk functions (see the vignette "Bayesian_lgcp"); specify the priors using lgcpPrior; and if desired, the initial values for the MCMC, using the function lgcpInits.

6. Run the MCMC algorithm and save the output to disk. We recommend dumping information to disk using the dump2dir function in the output.control argument because it offers much greater flexibility in terms of MCMC diagnosis and post-processing.

7. Perform post-processing analyses including MCMC diagnostic checks and produce summaries of the posterior expectations we require for presentation. (see the vignette "Bayesian_lgcp" for further details). Functions of use in this step include traceplots, autocorr, parautocorr, ltar, parsummary, priorpost, postcov, textsummary, expectation, exceedProbs and lgcp:::expectation.lgcpPredict

Value

an object of class lgcpPredictMultitypeSpatialPlusParameters

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle. Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R. Submitted.

2. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

3. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

4. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

5. Wood ATA, Chan G (1994). Simulation of Stationary Gaussian Processes in [0,1]d. Journal of Computational and Graphical Statistics, 3(4), 409-432.

6. Moller J, Syversveen AR, Waagepetersen RP (1998). Log Gaussian Cox Processes. Scandinavian Journal of Statistics, 25(3), 451-482.

See Also

linkchooseCellWidth, getpolyol, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, ltar, autocorr, parautocorr, traceplots, parsummary, textsummary, priorpost, postcov, exceedProbs, betavals, etavals

lgcpPredictSpatial function

Description

The function lgcpPredictSpatial performs spatial prediction for log-Gaussian Cox Processes

Usage

lgcpPredictSpatial(
  sd,
  model.parameters = lgcppars(),
  spatial.covmodel = "exponential",
  covpars = c(),
  cellwidth = NULL,
  gridsize = NULL,
  spatial.intensity,
  spatial.offset = NULL,
  mcmc.control,
  output.control = setoutput(),
  gradtrunc = Inf,
  ext = 2,
  inclusion = "touching"
)

Arguments